Curtate Cycloid
The path traced out by a fixed point at a Radius 
, where 
is the Radius of a rolling Circle,sometimes also called a Contracted Cycloid.
 |  |  | (1) |
 | |  | (2) |
The Arc Length from
is | (3) |
 | (4) |
 | (5) |
is a complete Elliptic Integral of the Second Kind and 
is aJacobi Elliptic Function.See also Cycloid, Prolate Cycloid
References
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., 1989. Wagon, S. Mathematica in Action. New York: W. H. Freeman, pp. 46-50, 1991.
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